Molecular Evolutionary Growth of Ultralong Semiconducting Double‐Walled Carbon Nanotubes

Abstract The self‐assembling preparation accompanied with template auto‐catalysis loop and the ability to gather energy, induces the appearance of chirality and entropy reduction in biotic systems. However, an abiotic system with biotic characteristics is of great significance but still missing. Here, it is demonstrated that the molecular evolution is characteristic of ultralong carbon nanotube preparation, revealing the advantage of chiral assembly through template auto‐catalysis growth, stepwise‐enriched chirality distribution with decreasing entropy, and environmental effects on the evolutionary growth. Specifically, the defective and metallic nanotubes perform inferiority to semiconducting counterparts, among of which the ones with double walls and specific chirality (n, m) are more predominant due to molecular coevolution. An explicit evolutionary trend for tailoring certain layer chirality is presented toward perfect near‐(2n, n)‐containing semiconducting double‐walled nanotubes. These findings extend our conceptual understanding for the template auto‐catalysis assembly of abiotic carbon nanotubes, and provide an inspiration for preparing chiral materials with kinetic stability by evolutionary growth.

In Rayleigh resonance scattering (RRS), a single carbon nanotube (CNT) owning a change in chirality or structure along its axial direction would show a color change accordingly, [1] which provides an efficient method to identify the chiral consistency. [2,3] The monochromatic characteristics at different positions of the CNTs on the substrate, as well as the consistent energy values of RRS peaks, elucidate the chirality remains consistent along the axial direction.
The air-suspended CNTs that exclude the influence of substrate also behave homogeneous color in the RRS images, demonstrating the reliability of monochromatic characteristics ( Figure S2). Furthermore, the high density of air-suspended CNT arrays and the ability of crossing even 6mm-wide trenches in the flying-kite growth, can also prove the growth stability and perfect structure of the CNTs ( Figure S4).
Supporting Section 2. The calculation of the number of 'generations' based on the length of ultralong CNTs Each round of circumferential atomic assembly during the CNT growth can be regarded as the production of a new 'generation'. For CNTs, each round of circumferential atomic assembly yields a length increment in the direction of the tube axis, which can be described as ( Figure   S5): where  is the chiral angle, C C a  is the distance between neighboring two carbon atoms in CNTs and is usually considered as 0.14 nm.
The value of cos(30 )    falls in the range from 3 2 to 1 in the whole range of chiral angle  . As the range from 3 2 to 1 is not large and the length of nascent seeds for ultralong CNTs can be neglected, thus the number of 'generations' for ultralong CNTs can be calculated as , where L is the length of ultralong CNT.

Supporting Section 3. The calculation of Euclidean distances for different types of CNT
We adopt Euclidean distance, a valid and widely-used parameter for characterizing the divergence among different species or populations in biology and ecology, [4,5] to measure the evolutionary divergence among different kinds of CNTs. Different types of CNTs contain the ones decaying in different length interval, which represents the survival time and iterative generations. Thus, the Euclidean distances in this work were calculated by: where 12 D is the Euclidean distance between the CNTs of type 1 and type 2, 1 j N , 2 j N are the number density of CNTs decaying in the length interval j, and j=1 to p are the length intervals where we collected the statistics of number density N.
For example, the Euclidean distance between s-CNT and m-CNTs was calculated based on the number density listed in Supporting

Supporting Section 4. Identify the chiral indices by combing RRS and Raman spectra
Combining RRS with Raman spectra could help to identify chiral indices of CNTs, with higher reliability and accuracy. Based on the resonance peaks resolved from RRS spectra, we can identify the energy resonant with CNTs and choose an appropriate laser to conduct Raman spectroscopy characterizations. The resonant energy values and RBM positions of Raman spectra under different excitation wavelengths can be used to assign the chiral indices of CNTs by consulting the atlas, [6] while the shape of G band would also help distinguish s-and m-CNTs.

Supporting Section 5. Different segments of operating process of chemical vapor deposition (CVD) preparation
The actual operating process of CVD preparation can be mainly divided into reduction segment, reaction (growth) segment and cooling-down segment. The setups of temperature and gas flow in each segment are schematically shown in Figure S8, to help understand the in-situ mass spectra in different stages.
Supporting Section 6. The analyzation for in-situ mass spectra to identify the key role of

C2H2
We used in-situ mass spectrometry to monitor the atmosphere and identify key factors in the CVD process.
Typical in-situ mass spectra in the growth with pure CH4 are shown in Figure S9c. In the reduction segment, the air in the reactor has been extruded out, verified by the blank at mass number m/z = 28, 29 that indicates N2 or C2H4. Then in the reaction segment, the signal at m/z = 28 could confirm the existence of C2H4. And the relative weaker signal at m/z = 29 due to the isotopic distribution can also be identified as C2H4. Furthermore, a small amount of C2H2 was found at m/z = 26 and 27. The relative intensity of C2H4 and C2H2 peak is also consistent with previous research. [7] Furthermore, the growth states with different CVD parameters are related to the intensity of C2H2 and C2H4 peak. Specifically, CNTs decayed less rapidly in batch 1, with a number density N at 15-mm-length position of 2.54/100 μm, much higher than the 1.28 for batch 2 ( Figure S9, a and b). While the C2H2 and C2H4 peak intensity ( Figure S9c) and the intensity variation from the reduction segment to the reaction segment ( Figure S9d) in batch 1 were also higher. Then we normalized the total peak area of C2H2 and C2H4 based on the peak area of Ar. Finally, we quantified the number density at 15-mm-length position versus the normalized total peak area of C2H2 and C2H4, respectively ( Figure S9e). The number density increases with the peak area of C2H2 and C2H4, behaving positively-related dependences. While exerting similar effect on the growth, the total amount and the variation of C2H2 are also much smaller than C2H4. These phenomena and the high-energy feature of C2H2 demonstrate that C2H2 is of greater significance to the out-of-equilibrium template auto-catalysis (TAC) growth. Besides, alkynes have been shown to accelerate the growth of vertically-aligned CNTs and thought to be related to the autocatalysis. [8] Thus, introducing a small amount of C2H2 is necessary to investigate its effect, without drastic alteration to the original carbon source.
Supporting Section 7. The enhancement effect of the introduction of a minor amount of

C2H2
The mass spectra revealed that the amount of C2H2 is about 1% of CH4, while exerting obvious effect on the growth. Therefore, we used ~1% C2H2 +~99% CH4 as the mixed carbon source. The experimental results demonstrated it could prominently enhance CNT growth, further confirming the key role of C2H2.
Firstly, the effective introduction of C2H2 and its volume percentage are verified by the mass spectra in cold state ( Figure S10a) and actual growth ( Figure S10b). The elongation growth with the mixed carbon source also owns a constant rate, slightly larger than that of CH4 ( Figure   S10c).
A typical SEM image of ultralong CNT arrays prepared with mixed carbon source ( Figure   S1a) manifests the parallel morphology, possessing a number density of 4.32/100 μm at 15mm-length position, exceeding that in Figure S9a by a factor of ~1.7. Besides, representative large-range overviews for as-prepared CNTs demonstrated the number density and growth persistence were enhanced by the introduction of a trace of C2H2 ( Figure S11).
The modified CVD growth involves ~1% vol substitution of C2H2, but much larger volume ratios of H2/mixed carbon source are found to be more advantageous for growth, thus the atom ratios of H/C are also increased. Therefore, the amount of available carbon atoms could not account for the unexpected increase of number density. It demonstrated the key role of C2H2, the direct supply of which with tiny amount can obviously promote the out-of-equilibrium autocatalysis of CNTs, compared with the pure CH4 situation, where C2H2 must be provided indirectly after the conversion.
Supporting Section 8. The evolutionary growth with pure CH4 carbon source In the growth with pure CH4 as carbon source, the chirality distribution also behaves an evolutionary trend. The chiral indices of CNTs are randomly distributed at first. As length increases, an obvious phenomenon of gathering along two discrete lines of (2n, n) and (n, n-1) appears, and the chiral indices are concentrated on fewer species gradually. The chirality distributions at multiple length positions are summarized in Figure S12. For example, at the position of 80 mm length, the abundance of chiral angle within 19.1° ± 5° reaches 40.4%.
Moreover, (n, n-1) and (n, n-2) species achieve a combined abundance of 56.3%. The distribution is almost balanced for the two lines. The gradually-decreased entropy can also be attributed to the continuous energy input, under the TAC mechanism.
Supporting Section 9. Representative performances of the as-manufactured CNT              Scale bar for inset, 5 μm.
Supporting Table 1 Number